How inconstant are climate feedbacks – and does it matter?

Kyle Armour has a new paper out in Nature Climate Change: “Energy budget constraints on climate sensitivity in light of inconstant climate feedbacks”.

Its two key claims are:

“global climate models robustly show that feedbacks vary over time, with a strong tendency for climate sensitivity to increase as equilibrium is approached. … I find that the long-term value of climate sensitivity is, on average, 26% above that inferred during transient warming within global climate models, with a larger discrepancy when climate sensitivity is high.”

“Moreover, model values of climate sensitivity inferred during transient warming are found to be consistent with energy budget observations, indicating that the models are not overly sensitive. Using model-based estimates of how climate feedbacks will change in the future, in conjunction with recent energy budget constraints, produces a current best estimate of equilibrium climate sensitivity of 2.9 °C (1.7–7.1 °C, 90% confidence). “

I will examine these claims in turn. But first I would like to point out that even if they were both sound (which on my analysis they aren’t), it would be almost entirely irrelevant to the level of temperatures in the final decades of this century, at least in scenarios in which greenhouse gas concentrations continue to rise until then. That is because up to 2100 warming will depend very largely on the level of the transient climate response (TCR), not on equilibrium climate sensitivity (ECS). The claims made by Kyle Armour have no bearing on TCR or on its estimation from warming over the instrumental period.

Armour’s first key claim

The first claim is entirely about the behaviour of atmosphere-ocean global climate models (AOGCMs), specifically the CMIP5 models used in the IPCC AR5 report. As these models take thousands of simulation years to equilibrate, their ECS is usually estimated from the results of a simulation in which atmospheric CO2 concentration is abruptly quadrupled immediately after the simulation starts (abrupt4xCO2). These simulations start from an equilibrium preindustrial state and usually cover 150 years. The top-of-atmosphere (TOA) radiative imbalance (N) is plotted against the change in global surface temperature (GMST or T), usually as annual means, over the course of the simulation – a so-called “Gregory plot”. Ordinary least-squares (OLS) linear regression is performed on the plot values and ECS (the equilibrium rise in T for a doubling of CO2) is derived as half the x-intercept.[1]

In AR5 the ECS of CMIP5 models was estimated by Gregory-plot OLS regression over years 1‑150 of abrupt4xCO2 simulations.[2] This method implicitly assumes that aggregate climate feedbacks are constant over time as well as independent of climate state (and hence of whether CO2 concentration is doubled or quadrupled).[3]

However, in about 90% of CMIP5 models, the slope of the Gregory-plot is steeper over the first few decades of the abrupt4xCO2 simulation than subsequently, pointing to net climate feedbacks weakening over time. This has led to an alternative estimate of their ECS, differing only in that the Gregory-plot regression utilizes only years 21-150 of the abrupt4xCO2 simulations, to capture models’ feedbacks after the early decades.[4] Kyle adopts this method for estimating models true ECS values.[5]

Figure 1 shows a Gregory plot for the GFDL-CM3 model, illustrating that the slope of the fitted regression line (representing net climate feedbacks, inclusive of the Planck feedback) is slightly lower, and the resulting ECS estimate slightly higher, using data from years 21-150 rather than 1-150 (and vice versa when using data for years 1-20 rather than 21-150). Figure 1: Example Gregory plot with regression line fits. ECS estimates are half the x-intercepts. Values for individual years are marked by open circles; dT generally increases with time.

Armour also estimates the effective radiative forcing (ERF) from a doubling of CO2 concentration (F2xCO2) by Gregory plot regression, as half the y-intercept from Gregory-plot regression using years 1-5 of the abrupt4xCO2 simulation data. I think it preferable to use regression over years 1-20 to estimate F2xCO2, [6] which in line with James Hansen’s finding that 10 to 30 year regression periods were best for this purpose.[7] Doing so gives results broadly in line with estimates based on fixed sea-surface temperature (SST) simulations, the other standard method of estimating ERF.

Kyle Armour then compares the ECS estimates from regression of abrupt4xCO2 simulation data with estimates (called ECSinfer) intended to reflect approximations to ECS derivable when forcing increases gradually, as over the historical period. He derives ECSinfer in models from changes in T, N and forcing (F)[8] over the first 100 years of simulations in which CO2 concentration rises by 1% per annum (1pctCO2), [9] taking 31-year averages, using the energy budget formula (Δ denoting a change):

However, recent research has confirmed that CO2 forcing increases slightly faster than logarithmically with concentration,[11] which implies calculating F2xCO2 as half the value derived from a quadrupling of CO2 concentration overstates its value (by 4.6% or so).[12]

The paper’s first main result is that ECS is on average 26% higher than ECSinfer in CMIP5 models; Armour also finds that the excess increases with both ECS and ECSinfer.

When I calculate ECS/ECSinfer using Kyle Armour’s F2xCO2 values, analytical forcing approximations and set of 21 CMIP5 models, I obtain the same 1.26 average ratio.[13]

However, when I use F2xCO2 values derived, IMO more satisfactorily, from regression over years 1-20 of abrupt4xCO2 data rather than years 1-5, and estimates of CO2 forcing that allow for its slightly faster than logarithmic relationship with concentration, the mean ECS/ECSinfer ratio falls to 1.20. When I include all 33 CMIP5 models for which I have data, the average ratio reduces further, to 1.16.

The distribution of the ECS/ECSinfer ratio is quite skewed; as Kyle Armour reports, it rises with ECS. For models with an ECS of 3°C or less, the average ratio is only 1.07. It is generally considered appropriate to use the median rather than the mean as a central measure for skewed distributions.[14] The average is inflated by an extremely high ECS/ECSinfer ratio for the highly sensitive CSIRO-Mk3-6-0 model. The median ECS/ECSinfer ratio is only 1.12, under half Kyle’s 1.26 average value.

Even if ECS were as high as it is in the median CMIP5 model (3.2°C), using instead the ECSinfer value of 3.2 / 1.12 = 2.86°C when projecting warming over the next century or two would make very little difference on non-mitigation or strong mitigation scenarios. Armour’s results end to support this, at least over the next century, in that they show that ECS/ECSinfer changes very slowly over time under (1% p.a.) CO2 ramping.[15]

There is as yet no observational evidence that climate sensitivity increases with time in the real climate system – although this cannot be ruled out – nor is it fully understood why it increases in most AOGCMs. In any event, even if real-world climate sensitivity does increase with time, in the longer run other factors that are not reflected in ECS, such as melting ice sheets, are probably more important. Therefore, while time-varying climate sensitivity is of considerable interest from a theoretical point of view, for practical purposes its influence is likely to be very modest.

Armour’s second key claim

It does not follow, from model values of climate sensitivity inferred during transient warming being are found to be “consistent” with energy budget observations, that in general the models are not overly sensitive.[16] By “consistent” Kyle Armour means that the 5-95% uncertainty range of observationally-based energy budget ECS estimates spans the full CMIP5 model range of ECSinfer. This is broadly true, but of limited relevance.

What is much more important is whether the two distributions are concentrated around values close to each other or not. For both our sets of CMIP5 models, I calculate the median (and mean) ECSinfer value as 3.0°C.[17] This is well above median estimates, of ECSinfer as a proxy for ECS, from the highest quality energy budget studies based on warming over the historical period: Otto et al. 2013’s best two estimates were 1.9 to 2.0°C. Lewis and Curry 2015’s median estimates, based on IPCC AR5 forcing and heat uptake data, were all 1.6°C or 1.7°C, depending on period used. An update I blog-published last year gave a median ECS estimate of 1.74°C. If the globally-complete Cowtan & Way infilled version of the HadCRUT4 surface temperature dataset is used instead of the original, this ECS estimate becomes 1.9°C. This is a long way below the median CMIP5 ECSinfer value of 3.0°C.

Armour’s 2.9°C ECS best estimate (although not the uncertainty range) is obtainable simply by (a) scaling up the ECSinfer value resulting from applying the energy budget formula to the Otto et al. observational constraints, being 1.99°C, by the 24% adjustment factor for ΔT that Richardson et al. (2016) derives, giving an ECSinfer estimate of 2.47°C (which agrees to Armour’s Table 1, first row); and then (b) multiplying by 1.1945, the fitted ratio of ECS/ECSinfer per Armour’s equation (5), which relates the ECS/ECSinfer ratio to the value of ECSinfer.

I don’t accept that the Richardson et al. 24% warming adjustment is realistic; see my critique of that study here. Moreover, Armour’s equation (5) is actually of little use in estimating how ECS/ECSinfer varies with ECSinfer; for his set of CMIP5 models the equation (5) fitted values explain only 4% of the variance in ECS/ECSinfer.

I’m not in any event sure how useful it is to produce a best estimate of ECS (as opposed to ECSinfer) from instrumental period observational data, since not only can ECS/ECSinfer only be estimated in AOGCMs but the ratio varies widely between different AOGCMs.

Conclusions

I like Kyle Armour and respect him as a scientist, but I think this paper’s primary finding is greatly overstated and that applying it using the questionable Richardson et al. 24% adjustment to warming measured by HadCRUT4 does not produce a very meaningful secondary finding.

It has in fact been found that when CMIP5 models are forced with specified SST anomalies matching the pattern of warming over the historical period, they produce net climate feedbacks of the order of 2 Wm-2K-1, closely consistent with the modest ECS best estimates from good observationally-based energy budget studies.[18] The real questions seem to be why do AOGCMs simulate very different warming patterns under increased CO2 concentration than those that have actually occurred during the historical period, and why do their net feedback strengths differ so much between these warming patterns.

Acknowledgements

Kyle Armour kindly shared the final version of his paper with me earlier, thus facilitating my analysis and enabling us to have a useful discussion about his paper and my analysis. Kyle Armour has seen an earlier draft of this article and, although he does not concur with the choices that I have made in my analysis, he has provided helpful comments.

Notes and references

[1] The logic here is that when N is zero the model will have reached equilibrium, and that CO2 forcing is logarithmically related to its concentration so that forcing from a quadrupling of CO2 concentration is twice that from a doubling.

[3] It also assumes, by the use of OLS regression, that internal variability in the regressor variable T is small enough to be ignored. It further assumes that T and N (a) have been correctly adjusted by deducting their equilibrium absolute levels in preindustrial conditions; (b) that any drift in those levels is constant over time and has been correctly adjusted for; and (c) that any imbalance in N in equilibrium, due e.g. to energy leakage in the model, is independent of the model’s climate state. Estimation of ECS by running the simulation until equilibrium is also dependent on assumptions (b) and (c).

[5] Although Kyle Armour twice states in the paper (Methods) that he estimates model ECS by regression over years 121-150 of abrupt4xCO2 simulations, he has confirmed to me that this is an error and that he actually used regression over years 21-150. The ECS values in Supplementary Table 1 are fairly closely in line with my own estimates from regressing over years 21-150.

[6] During year 1, the initial instantaneous radiative forcing reduces to reach ERF, as stratospheric, tropospheric and fast land surface adjustments (such as CO2-induced stomatal closure, which reduces evapotranspiration and affects soil moisture) to the increase in CO2 concentration, unrelated to surface temperature, take place. Accordingly, including year 1 in a regression to estimate F2xCO2 does not produce pure ERF estimation. Year 1, which often lies above the years 1-20 regression line, has a much larger impact on 5 year regression. Years 1-5 regression estimates are accordingly usually rather higher than year 1-20 estimates, on average by 5% for the 34 CMIP5 models that I have abrupt4xCO2 data for (by 7% for the subset of 21 models studied by Kyle Armour). Regression over years 1-5 is also much more affected by interannual variability. The mean and median CO2 ERF in CMIP5 models derived by regression over years 1-20 lies between that estimated from regression over years 2-5 and 2-10, before any material change in model’s net climate feedback occurs.

[8] Armour states in the paper that he uses an analytical approximation for forcing as time t years into the 1pctCO2 simulation: ΔF(t) = F2xCO2 *t/69, which would marginally overstates ΔF (and hence understate ECS infer) even if the underlying assumption that CO2 forcing increases exactly logarithmically with forcing is correct; the doubling time for a 1% per annum rate of increase is 69.7 years. In fact, he used a divisor of 70 years, not 69 years (pers. comm.), which has a opposite but milder effect, but which appears to be cancelled out by his similarly taking the mean value for t as 100 years rather than the exact 99.5 years.

[9] I generally use regression over years 1-30 of abrupt4xCO2 simulations to estimate ECS as inferred from historical warming, as the signal-to-noise ratio is much higher in abrupt4xCO2 simulations than in 1pctCO2 simulations. Doing so fairly reflects the circa 30 year weighted average period since each year’s forcing increment arose. On average, the resulting estimates are within 1% of those I estimate from 1pctCO2 simulations on the same basis that Kyle Armour uses.

[10] The paper uses the change ΔQ in the rate of increase in global heat content rather than ΔN, but these two variables have virtually identical values in the real world, and should do in AOGCMs.

[12] Assuming CO2 is the only greenhouse gas being increased. At year 100 of the 1pctCO2 simulations, when CO2 concentration has increased by a factor of 2.7, the ratio of CO2 forcing to its level when its concentration it quadrupled is ~2% short of a logarithmic relationship.

[13] This is so whether using his Supplementary Table 1 ECS values or those I calculate myself from Gregory-plot regression over years 21-150. All of my ECSinfer values are within 2% of his, save for one that is 5% lower.

[14] This issue was considered by the AR5 authors in relation to observational estimates of ECS, which also have skewed distributions; they likewise favoured use of the median rather than of the mean.

[15] Armour quantifies this in the final paragraph of the Methods section.

[16] Moreover, Armour bases this claim on a CMIP5 range for ECSinfer of 2.1-3.8°C, whereas on my calculations the range is 2.1-4.4°C, or 2.0-4.4°C taking all 33 models.

[17] On my calculation basis but adjusting the CO2 forcing non-logarithmic factor for appropriate comparison with observationally-based ECS estimates rather than halved estimate of equilibrium warming in abrupt4xCO2 simulation.

229 responses to “How inconstant are climate feedbacks – and does it matter?”

The interpretation that observational estimates of ECS_{infer} constrain the equilibrium climate sensitivity, ….

depends on a key, but often unstated, assumption: that the global
climate feedback in operation when equilibrium is reached, lambda_{eq},
will be equal to the feedback in operation at any given time, lambda.

is, however, an important point. If this assumption is wrong (as is suggested) then the ECS inferred from observations will be different to that when we have reached equilibrium and, as is also suggested, will probably underestimate the actual ECS.

I also don’t think that this claim

The claims made by Kyle Armour have no bearing on TCR or on its estimation from warming over the instrumental period.

is correct. The effect on the TCR would probably be smaller than on the ECS, but I don’t think it has no bearing.

You are quite wrong about TCR; time varying feedbacks are not relevant to TCR estimation, since the length of the available temperature and forcing data records is not shorter than the 70 year warming period that is implicit in the definition of TCR.

Except observational estimates of the TCR are not based on 1% per year increases over 70 years. If Armoour is correct that the feedacks in the future may not be the same as they have been to date, then an observationally based estimate for the TCR done today may also underestimate the actual TCR.

that the feedacks in the future may not be the same as they have been to date,

So, now, just because we have thermometers and computers, the basic physics of climate has or will change, I don’t really believe that is correct. What has happened will happen and due to the same causes as in the past, we are on earth as a flea is on an elephant, of little bother.

YOU SHOULD BRUSH UP ON WHAT CLIMATE IS: -”there is no such a thing as ‘’earth’s global climate’’ – there are many INDEPENDENT different MICRO CLIMATES 1] Alpine climate 2] Mediterranean climate, 3] sea- level climate 4] high altitude climate 5] temperate climates 6] subtropical climate, 7] tropical climate 8] desert climate 9] rainforest climates 10] wet climate 11] dry climate, as in desert AND THEY KEEP CHANGING; wet climate gets dry occasionally b] even rains in the desert sometimes and improves. In the tropics is wet and dry -/- in subtropics and temperate climates changes four time a year, WITH EVERY season= migratory birds can tell you that; because they know much more about climate than all the Warmist foot-solders and all climate skeptics combined – on the polar caps climates change twice a year. Leading Warmist know that is no ”global warming” so they encompassed ”climatic changes” to confuse and con the ignorant – so that when is some extreme weather for few days on some corner of the planet, to use it as proof of their phony global warming and ignore that the weather is good simultaneously on the other 97% of the planet, even though is same amount of co2. In other words, they used the trick as: -”if you want to sell that the sun is orbiting around the earth -> you encompass the moon – present proofs that the moon is orbiting around the earth and occasionally insert that: the sun and moon rise from same place and set to the west, proof that the ”sun is orbiting around the earth” AND the trick works, because the Flat-Earthers called ”climate skeptics” are fanatically supporting 90% of the Warmist lies. Bottom line: if somebody doesn’t believe that on the earth climate exist and constantly changes, but is no global warming -> ”climate skeptic” shouldn’t be allowed on the street, unless accompanied by an adult. b] many micro-climates and they keep changing, but no such a thing as ”global climate”

Are you more convinced by people who show no signs of doubt?
Philosophically a good point – we live with uncertainty.

However, advocates, a group of which I consider you a member, seem to have little doubt that CO2 will cause not just warming, but problems, and problems so in excess of benefits that limiting CO2 is necessary. And they remain doubtless often in the face of contradictory observations.

I have a problem with the terminology used in climate sensitivity. Equilibrium Climate Sensitivity (ECS) seems to be an incorrect use of terms. The climate system is better described as a steady state than an equilibrium. In my mind an equilibrium doesn’t loose or gain significant energy. With the sun constantly exchanging energy with the earth, and the earth constantly exchanging energy to space, I am really confused as to how equilibrium is the proper term for sensitivity to CO2 in a system that behaves like a text book steady state. I realize that ECS is the standard wording used, but what is the justification for that?

In this case, equilibrium refers to a state in which we would be losing as much energy per square metre per second as we were gaining from the Sun – i.e., energy equilibrium. You’re right that we will never be in true equilibrium, but the system will always be tending towards that state, even if it never actually attains it. It is still a useful metric for illustrating how sensitive the climate is to external perturbations.

atandb: That is by definition a steady state when energy in equals energy out.

A bunch of us have made that point over the years. In fact, it isn’t even a steady state, but at best an “approximate” steady state, where the temperature in each part stays within bounds but fluctuates, as the energy flows in and out fluctuate.

Is there any reason to think that the “equilibrium” concept approximates anything in the Earth’s climate? Equilibrium-based results abound because they are often computable (e.g. the Clausius-Clapeyron moist lapse rate), but they are sometimes clearly not accurate (e.g. the Clausius-Clapeyron moist lapse rate.)

If “climate” is the spatio-temporal distribution of the weather, sure. We have estimates (aka “measurements”) around the Earth, and summaries like means, standard deviations, minima, maxima, quantiles, and so forth.

But the Earth climate is clearly never in equilibrium, so the question is: what in the real climate, if anything, is accurately estimated by the computed model-based “equilibrium”?

Consider “the distance from the Earth to the Moon”: if it is the mean distance between the two centers of gravity, those can be estimated from models to useful degrees of approximation, and at any given time the “actual distance” may be close enough to the mean distance for practical purposes such as moon landings. Humans have lots of experience doing those calculations and showing that the calculations are reliable enough.

In the case of “equilibrium”, the evidence showing that it is a useful approximation to anything in the Earth Climate system is much more sparse.

There somewhat of a seasonal lag ( deficit during northern winter, surplus during northern winter ), so earth as a whole is always a few W/m^2 out of balance most of the year, but annualized, close to balance.

However, that’s not what climate is about. Climate are about how almost all places on earth are perpetually out of radiative balance and that imbalance is resolved by fluid flow from within:

The polar deficit and tropical surplus result from earth being an orbiting spheroid and this is not significantly altered by a nominal greenhouse gas increase. So, global warming is real, but climate change is not.

But even without changes in external forcing, the climate may vary naturally, because, in a system of components with very different response times and non-linear interactions, the components are never in equilibrium and are constantly varying. An example of such internal climate variation is the El Niño-Southern Oscillation (ENSO), resulting from the interaction between atmosphere and ocean in the tropical Pacific.

The balance is maintained for every spot on earth and in the oceans and in the atmosphere, it is different in different spots and it is constantly changing, but every spot is in balance at that time. that is how in balance works.

Equilibrium vs steady state: the delta entropy is not zero. Radiation scattering and dissipation does change entropy but how much is not clear. Christopher Essex did a few papers on this starting in 1984.

For what climate scientists mean when they discuss an “equilibrium climate”, go to Figure 3.2 (and surrounding text) in FAR here.

It really should be obvious that climate scientists aren’t using “equilibrium” to describe a completely isolated, isothermal system just as it should be obvious to first year physics students that the prof. doesn’t actually think textbook thermodynamic equilibrium ever actually happens or persists in the real universe.

The dictionary definition of “equilibrium” is “a state of rest or balance due to the equal action of opposing forces or “equal balance between any powers, influences, etc.; equality of effect”. Thus to talk of a thermal equilibrium where the amount of energy radiated is in balance with the amount of energy received fits perfectly within the definition of equilibrium, as there is a balance in opposing influences/effects.

atandb continues “That is by definition a steady state when energy in equals energy out.

I looked up the dictionary definition of “steady state” as well, and it gives:

“(physics) the condition of a system when some or all of the quantities describing it are independent of time but not necessarily in thermodynamic or chemical equilibrium See also equilibrium (sense 6)”

which is at variance with atandb’s definition as you can have energy in balancing energy out without either being independent of time (they can vary in time but be perfectly correlated). Note you can have equilibrium without steady-state and you can have steady-state without having equilibrium (according to the dictionary).

atandb continues “The use of the wrong term only leads to confusion.”

Indeed, which is why dictionaries are so useful.

atandb aslo wrote ” In my mind an equilibrium doesn’t loose or gain significant energy. With the sun constantly exchanging energy with the earth, and the earth constantly exchanging energy to space, I am really confused as to how equilibrium is the proper term for sensitivity to CO2 in a system that behaves like a text book steady state.”

As I understand it (I am not a physicist), all matter (with the possible exception of dark matter?) above 0K radiates energy, so if you are going to define “equilibrium” as neither loosing or gaining (significant) energy, then I think it is likely to be of somewhat limited utility, as it won’t be true of any system at the sort of temperatures we are likely to encounter on a daily basis.

A rather lengthy exchange based – mostly – on atandb apparently not even bothering to read my comment. Well, maybe they did, but “losing as much energy …. as we were gaining” is pretty clearly the same as “energy in equals energy out”.

yes, this sort of quibbling is an effective technique for avoiding discussion of the central issue, and makes rational discussion of science at most climate blogs an essentially pointless exercise.

The thing about the climate system never being at exact equilibrium is similar, there is no such requirement for ECS to be a useful measure of the response of the climate system to changes in the forcings. It is impossible to draw an exact circle in the real world, but that doesn’t mean it isn’t a useful concept. Likewise nothing in nature is truly Normally (i.e. Gaussian) distributed, arguably nothing above quantum level (and possibly not even there) is truly random, there is no such thing as an exactly unbiased coin, etc. etc. etc. However people rarely seem to have a problem with that! ;o)

Imagine that, the utility of equilibrium in climate is being argued again.

Equilibrium assumption is a useful tool. Without a doubt and since the assumption is based on some absolute temperature, humidity and energy input, temperature anomaly isn’t useful unless the system starts at equilibrium. Karl et al 2016 changed the initial absolute temperature of 70% of the surface by enough to offset 100% of the land measure energy change. Remember it is Ein versus Eout not Tin versus Tout.

If you don’t start at a condition that can be reasonably approximated as in equilibrium, then you don’t have a simple bounded solution, you have a changing reference energy where some portion is due to uncertainty in the reference equilibrium and some portion is due to the estimated anthropogenic change in energy output. If you initially “ASSUME” Tsurface is 15C = 390 Wm-2, but the surface is 14C = 390Wm-2 then you can have an error equal to the magnitude of the estimate effect.

In that case, the Equilibrium assumption isn’t valid or useful. When the error is small compared to the effect being measured, it is useful. So the real question should be how useful is the equilibrium assumption in this case, not citing thousands of cases where it has been useful.

dik, “The thing about the climate system never being at exact equilibrium is similar, there is no such requirement for ECS to be a useful measure of the response of the climate system to changes in the forcings. It is impossible to draw an exact circle in the real world, but that doesn’t mean it isn’t a useful concept. Likewise nothing in nature is truly Normally (i.e. Gaussian) distributed, arguably nothing above quantum level (and possibly not even there) is truly random, there is no such thing as an exactly unbiased coin, etc. etc. etc. However people rarely seem to have a problem with that! ;o)”

Kind of like coal can never be 100% clean and if you can measure small enough quantities, everything is a pollutant. It is almost like there needs to be some tolerances used to define how useful, how clean, how dangerous etc. to put things into perspective.

To be clear the difference between equilibrium and a steady state is that in equilibrium if the system is isolated the system will not change in temperature, pressure, volume, etc. So in the case of the earth, if you isolated it from the sun, it would cool, thus it is not in equilibrium. If you look at a dictionary definition of a technical term, many times it will be slightly different from the technical way that it is used by scientists. Confusing equilibrium and a steady state is pretty common for people not in the sciences. However, in Physics the definitions are very precise. A steady state can have energy flowing through the system such as is the case of the earth. Equilibrium by definition does not have significant energy flowing through the system. Trying to calculate the steady state climate sensitivity may make sense, but the equilibrium climate sensitivity does not.

Dictionary definition of equilibrium
“a state in which opposing forces or influences are balanced”
This is the sense used in climate. The incoming and outgoing radiation are balanced when at the equilibrium temperature.

Because I doubt it’s a question climate science needs to answer, Matt. That’s why I was speaking of idealizations and posits. What to do with these constructs is more relevant than if they refer to anything in reality.

What are numbers numbers of? Mathematicians all over the world do mathematics everyday without bothering to ask themselves about the nature of numbers. The same applies to the ideal gas law.

JimD, The issue isn’t how equilibrium is defined, it is what assumptions are made using the assumption. I believe it is called sensitivity of error. Right now the imbalance is estimated to be about 0.6 Wm-2 +/- 0.4Wm-2 at the top of the atmosphere which is approximated to be about 20km. Oddly, the imbalance is not uniformly distributed, but primarily in the southern hemisphere which just happens to receive the peak solar insulation and have the most ocean area with a nice dark albedo. Some portion of the imbalance could be related to the processional cycle. Some portion of the imbalance could be related to longer term ocean oscillation, Neither would have a huge temperature impact, but 0.2 Wm-2, about one third of the imbalance could be related to some unknown factor since nearly all ocean paleo reconstructions indicate about one half of a degree temperature variations on paleo data points sampled 50 years or more apart, super imposed on larger temperature variations 1500 to 5000 years apart. This makes for some interesting issues since the imbalance of ~0.6 Wm-2 is small compared to the +/- 17 Wm-2 at the surface.

Surface temperature anomaly is supposed to be related to imbalance assuming that it should be zero, but Paleo ocean reconstructions of the tropical oceans indicate there has been heat uptake for several hundreds of year and there might a slight acceleration recently related to anthropogenic causes.

Now you have about 1 trillion dollars on the line or about 100 billion to 500 billion per tenth of a Wm-2. Do you take door number 2 or door number 3?

atandb wrote “If you look at a dictionary definition of a technical term, many times it will be slightly different from the technical way that it is used by scientists.

O.K., from definition of “equilibrium” in the Oxford Dictionary of Physics (6th edition):

“A body is said to be in thermal equilibrium if no net heat exchange is taking place within it or between it and its surroundings. … These are examples of dynamic equilibrium, in which activity in one sense or direction is in aggregate balanced by comparable reverse activity.”
[emphasis mine]

which directly contradicts your usage. At the equilibrium relevant to the definition of ECS, the Earth is at thermal equilibrium because there is no net transfer of heat between the Earth and its surroundings (i.e. space); the amount of energy absorbed from space is equal to the amount radiated back out into space.

The dictionary of physics does not appear to give a direct definition of steady state, which suggests that it has no specific use in physics, other than that of everyday English. The clue is in the words “steady state” – the state of the system is steady (i.e. unchanging). Thus Fred Hoyle’s idea of a steady-state universe is called that because the theory suggested that the properties of the universe (e.g. its mean density) are unchanging, it is the same now in terms of its properties as it always has been. This wouldn’t be an equilibrium though as it requires the constant creation of matter to accommodate the observed expansion of the universe.

“Confusing equilibrium and a steady state is pretty common for people not in the sciences.”

indeed.

However, in Physics the definitions are very precise.

Fine, give me a verifiable reference to support your definitions of these terms.

Expansion of the universe does not entails neither creation nor destruction of matter/energy. It is a simple dilution into a larger volume. The only thing created is distance between galactic super clusters.

@David Springer it does if you want constant mean density, which is what Hoyle’s theory argued (Hoye’s theory was discredited long ago, but it is still a useful example of what it meant by “steady state” in physics).

> My question can be rephrased: What measurements on Earth could you use to determine whether a computed equilibrium temperature was computed accurately.

That’s not the same question as what in the real climate, if anything, is accurately estimated by the computed model-based “equilibrium”, Matt. The first one is about the object which you seek to estimate accurately. The second is about the empirical apparatus to insure the accuracy you seek.

Clarity and all that jazz.

To borrow NicL’s ringtone if his actual sleight of hand, I suspect the accuracy you seek is of little relevance. So both questions are of little relevance.

Lowballing sensitivity with the lowest justified disingenuousness money the GWPF and other energy think tanks can buy is more than risky business. It is barely rational.

Willard: To borrow NicL’s ringtone if his actual sleight of hand, I suspect the accuracy you seek is of little relevance.

I am always harping on the necessity for models to be shown to be accurate. See, for example, my comments (and some references) on Michaelis-Menten kinetics. Sufficient accuracy is a necessity for usefulness.

dikranmarsupial: “(physics) the condition of a system when some or all of the quantities describing it are independent of time but not necessarily in thermodynamic or chemical equilibrium See also equilibrium (sense 6)”

which is at variance with atandb’s definition as you can have energy in balancing energy out without either being independent of time

That definition is vague. Usually it is intensity variables that are independent of time (temperature, concentration) while aggregates are flowing through (heat, chemicals.)

dikranmarsupial: It is impossible to draw an exact circle in the real world, but that doesn’t mean it isn’t a useful concept. Likewise nothing in nature is truly Normally (i.e. Gaussian) distributed, arguably nothing above quantum level (and possibly not even there) is truly random,

People test the accuracy of those approximations all the time. For planetary orbits, ellipses are better than circles. For studying extremes, use the generalized extreme value distribution, not Gaussian.

matthewmarler writes “That definition is vague. Usually it is intensity variables that are independent of time (temperature, concentration) while aggregates are flowing through (heat, chemicals.)”

missing the point, which is that it is the independence of time on some property of interest that defines steady-state. In Hoyle’s steady-state universe the mean density of the universe is time-independent, but there is a constant flow of matter into an expanding universe. There is nothing in the definition of steady-state that assumes flows are zero, which is because that is not part of what defines steady state, which was the point being made. The flows may be zero, or they may not, it isn’t what defines steady-state AFAICS.

matthewrmarler writes:

dikranmarsupial: It is impossible to draw an exact circle in the real world, but that doesn’t mean it isn’t a useful concept. Likewise nothing in nature is truly Normally (i.e. Gaussian) distributed, arguably nothing above quantum level (and possibly not even there) is truly random,

People test the accuracy of those approximations all the time.

People test the GCMs, and their component elements, all the time, what do you think CMIP3/5 were? If you look, there are lots of *MIP projects, all of which are about comparing and evaluating models. See Table 6.5 of McGuffie and Henderson-Sellers, “A Climate Modelling Primer”, on page 229, which lists 37 such “Model Intercomparison Projects”. ECS being a constant is just saying that warming is approximately logarithmic in GHG concentration, once the system is approximately equilibriated. I think that assumption has been evaluated pretty well over the last century or so.

For studying extremes, use the use the generalized extreme value distribution, not Gaussian.

Given we are not talking about extremes, what is the relevance of this? The point I was making was that essentially nothing in nature is truly Gaussian, but it is still a very useful approximation. Applications of GEV are pretty much all applications were you know a-priori that the distribution of interest is no where near Gaussian, so that looks to me like an attempt to bluster away from the original point, which is that the definition of “equilibrium” used in “ECS” is perfectly reasonable.

matthewmarler earlier wrote “All of the energy that flows in flows out, or almost all; the system is not in equilibrium. . What you describe is “never far from steady state.””

It appears that matthew is not using the normal definition of “equilibrium” either, which suggests a discussion of whether ECS is meaningful is unlikely to be productive until that is corrected.

All objects above 0K radiate energy, so energy is always flowing out of more or less every object in the universe. So if a constant flow of energy flowing in and out of a body prevents it from being at equilibrium, there is nothing in the universe that is at equilibrium and the word is meaningless.

Of course you could look at the etymology of the word, from the Latin aequi – libra (“equal” and “balance” respectively). So what could it be that is in balance? Well the energy flowing in and the energy flowing out.

again, yet more inaccurate and irrelevant pedantry. For the earth to be in thermal equilibrium with its surroundings, all that is required is for there to be no net transfer of energy in or out. That means total energy in is balanced by total energy out, which doesn’t require symmetry either in space or temperature or that the radiation in or out is spatially homogenous.

“as nobody is claiming that the Earth is currently at equilibrium, that is just more irrelevant and inaccurate pedantry.”

Double speak versus pedantry, the never ending story of climate wonks.

The assumption of radiative equilibrium isn’t a useful tool unless the degree of imbalance can be related to some combination of physical influences. ASS-U-Ming there is a radiative imbalance and then ASS-U-Ming that the lack of radiate balance is due to “global surface temperature” being lower than it should be otherwise since the addition of GHGs, without knowing that there was a real radiative balance prior to the addition of the GHGs will result in some uncertainty.

So dik, can I call you dik, what portion of the existing imbalance is likely due to long term ocean recovery and why? Why is the imbalance limited to southern hemisphere oceans? Those are actually relevant questions based on what you imply is irrelevant, dik.

“Double speak versus pedantry, the never ending story of climate wonks.”

lack acknowledgement that nobody had claimed the climate is currently at equilibrium noted

“The assumption of radiative equilibrium isn’t a useful tool unless the degree of imbalance can be related to some combination of physical influences.

Assertion with no justification whatsoever. It is also incorrect, the concept (note it isn’t an assumption) of radiative equilibrium just means that total radiation absorbed equals total radiation emitted, and is entirely independent of the detailed physical mechanism responsible.

“ASS-U-Ming”“So dik, can I call you dik”

Yawn, I have seen this kind of childish rhetoric on climate blogs again and again. The only thing it tells me is that you are trying really hard to prevent any progress in discussing the science, which is a tacit admission that you don’t want progress as you know you are wrong. Sorry, life is too short, not remotely interested.

dik, “lack acknowledgement that nobody had claimed the climate is currently at equilibrium noted.”

The imbalance was originally assumed to be 1 Wm-2 and more recent studies reduced that estimate of ~0.6 Wm-2. A fairly recent Pages 2K study suggests that the tropical oceans start warming earlier than expected and that the southern oceans are gradually catching up.

Now let’s apply the knowledge and attempt to answer the questions instead of resorting to double speak. If half of the current imbalance is not due to CO2eq gases AND the magnitude of the imbalance is lower than initially expected, sensitivity would be lower than estimated. You could even expect “inconsistent climate feedback” if other mechanisms are involved. Now is that relevant or not dik?

It isn’t relevant, as I pointed out because nobody claims the climate system is at equilibrium, and the usefulness of ECS doesn’t depend on the climate system either being at equilibrium or actually reaching equilibrium in reality, or even our ability to measure the current radiative imbalance. It is an easy to understand single figure indication of the plausible sensitivity of the climate system to a change in the forcing.

“It isn’t relevant, as I pointed out because nobody claims the climate system is at equilibrium, and the usefulness of ECS doesn’t depend on the climate system either being at equilibrium or actually reaching equilibrium in reality, or even our ability to measure the current radiative imbalance. It is an easy to understand single figure indication of the plausible sensitivity of the climate system to a change in the forcing. ”

Now there ya go, the assumption of equilibrium is irrelevant. I knew you could do it. Now since “global mean surface temperature anomaly” is another tool used to compare with the irrelevant TOA equilibrium, how irrelevant is it? How about the relevance of the “33C discrepancy?”

dikranmarsupial: However people rarely seem to have a problem with that! ;o)

I think my examples show that people worry about “that” all the time. Perhaps you meant only “random sample”, and not circle and Gaussian in that comment.

Flow through or lack of flow through is not in the definition of steady state. all the examples I have seen, and the example of Earth climate, includes flow-through.

“Equilibrium” climate temperature could be a useful approximation to the global mean surface temperature a (long) time after a change to the system. I am not sure that is what is claimed, and I am not sure equilibrium temperature has been shown to be an accurate approximation to anything.,

There was a Roman warm period, a cold period after that, the Medieval Warm period after that, the little ice age after that, now this normal natural and necessary modern warm period. We are in a warm period and the temperatures are warmer than the average because that is normal and natural in a warmer time period. To expect otherwise would not reflect any knowledge about the climate history.

Of the identified feedback mechanisms, ( Water Vapor, Lapse Rate, Ice Albedo, and Clouds ), all would appear to be Fast Feedbacks, which definitely imply front loading and decreasing sensitivity with time.

Slow feedbacks make the most sense. It snows more for many years when oceans are warmer and thawed, the ice piles up, spreads out and makes it colder. it snows much less for many years when oceans are colder and more frozen, the ice flows and melts and depletes until ice extent decreases and allows it to get warm again. This is not a fast process. in the most recent ten thousand years this cycle has been about a thousand years to repeat. In the past major warm periods and major ice ages this cycle has had tens of thousands of years of warm and a hundred thousand years of cold. You can look at actual ice core data and plot it for yourself.

This behaviour appears to arise from the fact that the global radiative response depends not only on global surface warming, but also on the time-varying spatial pattern of warming12,15,16. For example, the Southern Ocean has shown little warming to date, but is expected to warm substantially over the coming centuries13,25; consequently, λ will tend to decrease in the future as destabilizing Southern Ocean feedbacks (for example, ice-albedo) become activated12. Evolving sea-surface temperature patterns also appear to drive changes in tropical cloud feedbacks that further cause λ to decrease over time10,14–16.

It might help to consider that sea ice maxima occur in early spring in their respective hemispheres, and minima in early fall, TE. Cue to, “yabbut maximum Antarctic sea ice extent is increasing, not decreasing.”

***

For anyone following along who isn’t inclined to think climate researchers overlook basics that even random anonymous blog commenters know about, check Figure 5 from the (self-)cited reference:

> Yes, it would be nice to have confirmed observations rather than contradicted model runs.

It would also be nice to be omniscient, TE. Here in the real world, we just have to settle for doing science which entails the use of simplified and imperfect models. The beauty of this state of affairs is the cornucopian examples of predictions which don’t gibe with subsequent observation (or which haven’t manifest quickly enough to satisfy the arbitrary demands of lay critics) such as …

> Could also throw in the so far missing negative lapse rate feedback.

… yet the planet continues to warm just as Arrhenius predicted in the late 19th century using nothing more sophisticated than laborious hand calculations. If the nth-order effects were easy to suss out, everyone would be doing it and getting it right. It turns out that simulating planetary-scale weather/climate phenomena is difficult. Who knew!

> And the fact that the cloud and water vapor feedbacks are still not strictly verifiable because of poor observations.

And the problem with strict empiricism is that it precludes cautionary avoidance of unprecedented and *potentially* deleterious events before they can be verifiably realized.

***

Back to Antarctic sea ice, Eric Steig offers some thoughts on why growth in extent under a transient warming regime is only naively counterintuitive. It’s extensively referenced and contains a number of appropriate caveats. A main point is that Teh Modulz aren’t so Stoopid about sea ice extent when changes in wind patterns are prescribed …

… which does imply that Teh Modulz are still Stoopid. One of the included references (Holland et al 2013) agrees. However, unlike the hordes of amateur Modulz-bashers infesting blog comment sections, the authors are actually attempting to sort out the problems and thereby hopefully add to knowledge instead of doing their level best to amplify ignorance.

Yes, it would be nice to have confirmed observations rather than contradicted model runs.

“It would also be nice to be omniscient, TE. Here in the real world, we just have to settle for doing science which entails the use of simplified and imperfect models.”

The world’s religions also have models predicting salvation or damnation, but no confirmation. In this regard, climate models are not different.

“The beauty of this state of affairs is the cornucopian examples of predictions which don’t gibe with subsequent observation (or which haven’t manifest quickly enough to satisfy the arbitrary demands of lay critics) such as …”

Yes, religions also push out failed predictions to the safety of the future where they are not falsifiable and where the gullible can so keep the faith.

Could also throw in the so far missing negative lapse rate feedback.

“… yet the planet continues to warm just as Arrhenius predicted in the late 19th century using nothing more sophisticated than laborious hand calculations.”

Lowering the bar now. I did not question radiative forcing, or warming and this did not appear until you resorted to the straw man. The paper is about accelerating sensitivity which is conceivable, but very questionable. The hoax of CAGW is not the hoax of principle, but the hoax of exaggeration. The rates of warming are exaggerated and the implication of catastrophe is similarly an exaggeration ( including the ignorance of benefit ). The entire point of using GCMs is capture transfers within the atmosphere, but these are the very aspects which are failing to verify. This is not surprising given that motions of the atmosphere are known to be unpredictable.

“Back to Antarctic sea ice, Eric Steig offers some thoughts on why growth in extent under a transient warming regime is only naively counter intuitive.”
Yes, if one considers that Antarctic Sea Ice occurs with a contribution of cold air masses from the continent, then the wintertime Antarctic radiative cooling from increased CO2 makes increasing Antarctic Sea Ice entirely intuitive and a trend likely to continue as long as CO2 is increasing.

“It’s extensively referenced and contains a number of appropriate caveats. A main point is that Teh Modulz aren’t so Stoopid about sea ice extent when changes in wind patterns are prescribed …”
Yes, winds that general circulation models were explicitly applied to represent and understandably fail to replicate. Regarding the winds, the faithful will ascribe Antarctic sea ice increase to winds and Arctic sea ice decline to global warming and not circulation. Infidels probably the reverse.

The water vapor feedback is not immediate because it responds to the ocean temperature and that lags the global mean. Currently the ocean is only warming at half of the land temperature, and therefore rather slower than the global mean. It is because of this lag that TCR accounts for less of the water vapor feedback than the full ECS would because for ECS the ocean warming has caught up to the global mean.

Water vapor correlates quite well with temperature in the seasonal cycle ( within a month ), so there’s not a lag in feedback.

In fact, the reason the oceans don’t warm as fast as land, in addition to the greater thermal capacity, is that when exposed to increased radiance, the oceans cool by latent heat of evaporation – evaporated water bound for the atmosphere.

Where do you get that from, because it is plain wrong. In a transient climate the ocean can’t keep up with the land or the mean change. The amount of water vapor depends on the ocean surface temperature, and if that is warming more slowly, the global mean the relative humidity is decreasing while with water vapor feedback the equilibrium assumption is of a constant relative humidity. This deficiency of humidity in the transient state makes a difference.

JIm D: with water vapor feedback the equilibrium assumption is of a constant relative humidity.

That is one of several inaccurate propositions that follow from the equilibrium assumptions.

Turbulent Eddie: the oceans cool by latent heat of evaporation – evaporated water bound for the atmosphere.

Jim D:
Where do you get that from, because it is plain wrong.

Sometimes Jim D acknowledges the latent heat of evaporation, and sometimes not. More energy input is required to vaporize a KG of water at constant temperature than to raise its temperature by 1C. The cooling of the water surface by evaporation is considerable.

At temperatures characteristic of most of the ocean surface, water vapor pressure increases about 6% per C, so the water vapor feedback does not lag the temperature increase by much. In non-dry regions in the tropics, you can see the clouds forming not long after sunrise on sunny days.

Why should evaporation increase more quickly than the radiative forcing? Find a reference that says the ocean will not warm as much when in equilibrium. You won’t, because it is wrong. Even Arrhenius uses the Clausius-Clapeyron relation of 6-7% per degree, and that assumption is constant relative humidity, and those degrees are global mean degrees. If the ocean isn’t keeping up with the global mean, it won’t follow C-C on a global scale.

The way to cancel a radiative imbalance is surface warming. Nothing short of that works. Evaporation has no effect on the outgoing longwave at the top of the atmosphere. It counts for nothing in the top-of-atmosphere energy budget while a rise in surface temperature does. The global imbalance remains until the surface is warm enough to cancel it, and there is no reason for the water at a latitude to get cooler than the land in an annual mean sense. Given that we came out of an Ice Age, how much cooler did the ocean get than the land at the same latitude as a result of your purported evaporation increase? This is an off-the-cuff invention that you can’t support.

That latent heat is accounted for in the negative lapse rate feedback that is a response to the surface temperature increase, so the effect of more evaporation and latent heating is already built into AGW. What else do you have?

The way to cancel a radiative imbalance is surface warming. Nothing short of that works.

The reason the ‘hot spot’ is a negative feedback is that warming the upper troposphere works even better than warming the surface ( because most LW emissions that escape from earth take place aloft, not at the surface ).

Now, the surface and the upper troposphere are coupled, so they’re not likely to diverge too much for too long. But yes, warming the upper troposphere ‘works’ and even ‘works better’ than warming the surface. Also, humidifying the surface but drying aloft works – without raising surface temperature. And of course, increasing cloud albedo, for which there’s not a clear process, but also not much understanding, also works.

Warming the surface seems likely, but dogmatic exclusion of anything else probably closes you to the realms of possibility.

As I mentioned to Matthew Marler, the lapse rate feedback is already built into AGW. Since the ocean is not yet warming fully, the hot spot is slow to show, but when it does its negative feedback will kick in, but that only partially offsets the water vapor feedback that also kicks in. Bottom line: a delayed ocean response delays the water vapor feedbacks which are net positive.

Jim D: As I mentioned to Matthew Marler, the lapse rate feedback is already built into AGW.

I have posted enough already. If you think the lapse rate feedback that is built into the AGW sufficiently accounts for the transfer of H2O latent energy from the surface to the cloud condensation layer, so be it.

“Currently the ocean is only warming at half of the land temperature, and therefore rather slower than the global mean. It is because of this lag that TCR accounts for less of the water vapor feedback than the full ECS would because for ECS the ocean warming has caught up to the global mean.”

For ECS, the atmosphere has to drag the oceans with it if the oceans will follow. I would say they must but it will take a long time. If we accept that the oceans are warming half as fast, and at 1000 meters they don’t seem to be warming at that rate, the gap will increase, softening sensitivity the further the two are apart.

Where is ECS? In the oceans. They are the climate’s base, its home and its strength.

It is really the radiation that drives the ocean, not the air temperature. The heat capacity of the atmosphere is so much smaller that would be the tail wagging the dog. But the sustained few W/m2 from extra GHGs over years does sink into the ocean and warm it over time. It competes with overturning circulations, but wins out in the end.

Jim D | April 19, 2017 “The way to cancel a radiative imbalance is surface warming.”
On fire today Jim D, and making a very pertinent though unintended point.
The earth does not have a defined surface. Unlike say the moon where with low gravity and virtually no atmosphere, no lakes of water. the TOA is virtually the same as the surface.
The surface of the earth is actually a multi layer, multi media surface, 99.99997% of the surface atmosphere is below 100 km (62 mi; 330,000 ft), the Kármán line. By international convention, this marks the beginning of space.
Personally I think a definition of the surface of a planet/asteroid/black body etc should be those parts that are capable of receiving, reflecting or absorbing radiation.
Such a definition would reduce the surface of the moon to a few mm of depth whereas on earth the surface would be by definition 100 to 100.01 km thick as it would also include the depth to which it can penetrate the ocean say 100 meters for 99.99997 percent of the incident energy.
The point I am making is that the surface warming is just not at the surface commonly referred to by Jim D and most here but included the atmosphere itself.

The tropospheric temperature is also largely determined by the surface temperature through the physics of how the lapse rate is determined. In this sense, the only free variable to counter forcing is the surface temperature.

The tropospheric temperature is also largely determined by the surface temperature through the physics of how the lapse rate is determined. In this sense, the only free variable to counter forcing is the surface temperature.

No, IR from condensing water vapor at night is not constant, but adjusts as needed to limit cooling.

Their models are wrong and they don’t really care as long as the grants keep coming in. We elected Trump and a Republican Congress to stop spending tax money on this junk science, I do hope that does happen.

On that argument I would have chosen the mode rather than the median as the best estimate for ECS, since it is lower than the median. But I didn’t, even though the IPCC did so in AR4, because I regard the median as the appropriate measure (as, did the IPCC AR5 authors). .

Good luck selling the mode of a non-normal distribution as a central estimate.

***

> as, did the IPCC AR5 authors

Or, as written in the footnote: the AR5 authors in relation to observational estimates of ECS. Was it personal communication or is this traceable somewhere? As you belong to that collective, deferring to them looks a bit like double accounting.

In any case, as much as we need to respect those “AR5 authors,” they fail to pad the “generally considered” claimed in the text. One should expect something more “general” than that.

I have grave reservations about applying any statistical measures to the climate models. Statistics was founded on studying the mathematics of gambling, not on the mathematics of how much people thought they would win on their trip to Vegas. Considering all the fudge factors in the models, you might as well be talking about the average projected yacht size among people playing Powerball.

> It is obvious from AR5 WG1 Figure 10.20; the only central estimate it shows is the median.

“It” being the “generally considered” authority claim.

And now that authority claim is made “obvious” by looking at a graph.

FWIW, using medians could be pure convention.

***

> yes, there was a personal communication about this involved as well.

Then you write “pers. comm.” and paraphrase the arguments in favor. The usual crap about scale invariance, for instance. As if it mattered so much that investors would drop *weighted* averages. As if it lowballing sensitivity did not carry trillion dollars risks.

Another point Nic does not make above but does make in his excellent writeup on ECS is the issue of convection modeling in AOGCM’s. He points out that subtle changes the details of clouds and precipitation and convection can have a large effect on ECS. Since these parameters are very hard to constrain with data, one must conclude that the values used are educated guesses.

To me the importance of the paper is that it looks into effects of changes in the fundamental model assumptions as the other predicted changes occur.

It is always difficult to figure out what, in real life, the “equilibrium” refers to. Evidently, “equilibrium” is supposed to model the average temperature, even though no equilibrium ever exists.

The paper does not cite either the Romps et al paper or the Laliberte et al paper. Granted, we can not tell how general the Romps et al result is (about half the geographic area of continental US is modeled), but a 12% change in a surface to mid-troposphere energy flow is too important to ignore outright, I should think.

global climate models robustly show that feedbacks vary over time, with a strong tendency for climate sensitivity to increase as equilibrium is approached.

The climate scientists view climate as a dc electrical circuit and say there is high sensitivity near equilibrium.

The climate works like an ac electrical circuit. when it is crossing the midpoint, it is always headed for a peak or valley on the other side. just even just glance at ice core data. it snows more when it is warm and oceans are more thawed and after years of that, it gets colder. it snows less when it is cold and the oceans are more frozen and after years of that it gets warmer. There is no such thing as a midpoint equilibrium. any pause in change happens during the peak or during the valley. there is no pause when it is screaming across the midpoint. Look at actual data.

Ice ages are times with more ice, the snow that fell that caused it fell in the warm time before the cold time. Warm times are times with less ice, less snow fell in the cold time and allowed it the get warm.

Many forcing factors modify the cycles but they don’t cause or prevent the cycles. Only more snow in warm times and less snow in cold times force there to be regular warm and cold periods that always follow each other. ocean levels and ice accumulation in cold places has change and modified this cycle for 50 million years. we have the perfect balance between ice on land in cold places and ocean levels. This has been true for 10 thousand years and will continue.

The climate what will determine it from this point in time going forward is a very low solar/increased albedo /decrease overall sea surface temperature combination.
These in response to very low solar conditions which will promote less UV light cooling overall sea surface temperatures while an increase in major volcanic activity ,global cloud coverage/snow coverage will result in an increase in albedo. Even .5% increase in albedo would wipe out the natural warming that occurred from1840-2005 which was due to very active solar conditions throughout that time frame.

Already cooling is present and the sun has just started to approach my low average value solar criteria in order to accomplish this, despite some of the solar parameters remaining above my criteria that being the ap index/solar wind speed but those will be coming in line as sunspot activity diminishes which in turn will dry up coronal hole activity.

Also it is climatic thresholds that will cause a big climatic impact and those could be coming to some degree as we move forward.

To end ALBEDO trumps it all in my opinion, any change in it will have major climatic implications.

Regression lines infer linearity — which itself is a matter of conjecture — but, the real issue is that, global warming alarmism has always been a matter of what do you do after choosing the least significant contributor to global warming — CO2 — as that then requires creating mystical properties that are not observed in nature. The magic properties of CO2 are achieved by applying magical magnification formulae such that the scant contributor may become the source of a peril called AGW.

Good point… just because we’ve defined and named it–e.g., the average global temperature during the first and last half of the 20th century, doesn’t mean there will be anything we can do about what will happen in the future–e.g., we can divide up the years life into childhood and adulthood but there is nothing we can do to reverse the trend.

Regarding whether TCR increases over time, here’s hadcrut 4 vs forcing from 1900 to 1969. I didn’t downweight the volcanoes or adjust any other thing – it’s just the total forcing.

And from 1942 to 2011, the last year for which the IPCC provides forcings. The slope is basically the same (0.3% higher for the second period)

Obviously choosing two periods is a bit arbitrary; the best way would be to do a rolling regression to check every possible 70-year period (I don’t know how to do that in R). But these two periods cover all the time when there was strong forcing.

I never read any of theses things. It is a case of the very simple math that can be done. The drunk looking for his keys under the street light – because that’s where the light is.

The problem is that – in lieu of actual data on energy at top of atmosphere – it assumes all warming is anthropogenic. Actual toa data suggests something else entirely.

“The top-of-atmosphere (TOA) Earth radiation budget (ERB) is determined from the difference between how much energy is absorbed and emitted by the planet. Climate forcing results in an imbalance in the TOA radiation budget that has direct implications for global climate, but the large natural variability in the Earth’s radiation budget due to fluctuations in atmospheric and ocean dynamics complicates this picture.” https://link.springer.com/article/10.1007%2Fs10712-012-9175-1

So you can do the very simple math – but does it actually mean anything?

The theoretical limitations of models are even more certain. Non-linearities in equations of fluid transport dominate the evolution of solutions after short simulation periods.

Rowland et al 2012

All of these 1000’s of solutions of a single model are equally implausible. The solutions evolve from small initial differences on exponentially diverging pathways. You might pick one arbitrarily and send it to the IPCC – but what does it mean?

I have added a linear (thick black) extrapolation of the observed warming. It gives an upper estimate of near term warming potential. You could even estimate a sensitivity – but as it contains both natural and anthropogenic components I struggle with the futility of the exercise.

That is how it works, the equilibrium is always changing, but that is where we always are..
Worth repeating.
If CO2 has increased then the new forcing is there everyday when the sun comes up. It should not take 100 years to make a temperature adjustment to the new CO2 level. It should happen right away.
The fact that CO2 rise has been continulally uyp and Temp varies all over the place with no hint of being tied to the CO2 is a real concern.

The imbalance is important. If the imbalance is positive we are below the equilibrium for the current forcing level, and we know more warming will occur even if the forcing stays constant. So the important thing is the imbalance which is how far we are from equilibrium because that does make a difference to the temperature trend.

If one accepts that the imbalance if defined by the instantaneous integral of the global net radiative flux (positive or negative) at top of the atmosphere TOA, it’s only important to the extent one assumes future forcing is constant and predictable, as well as feedbacks.

It is easily conceivable that a positive imbalance today could turn to a negative imbalance tomorrow. A one in a century volcanic eruption could occur. Also the peak of an El Nino, like last years’s, could well have placed us into negative imbalance while Earth was radiating at peak temperatures. To know would take precise measurements of all areas of the surface hydrosphere.

Argo’s 3600 roving and floating thermometers should be the currently most productive tool in answering what the imbalance actually is relative to fluctuations in forcing and El Nino/La Nina (ENSO). Unfortunately it gives us only 11 years of data as of this moment. But yes, average likely future imbalance is one of the important considerations in determining observational TCR and ECS. For TCR we need to be able to isolate monthly global mean temperature GMST from ENSO’s sea surface temperature SST influence.

I am only saying the imbalance points to which side of the equilibrium we are on. The observed decadal trend of a rising ocean heat content is a positive imbalance and means we are below the equilibrium at the current decadal-averaged level of forcing. This is useful to know in itself, even if it seems obvious.

If there was any imbalance, it would show up in the CERES data and it does not. That means that the talk about the imbalance that does not exist is just idle talk and it means nothing other than alarmist stuff that is designed to just scare us.

OK, let’s assume you didn’t see note [10] by Nic Lewis.
“The paper uses the change ΔQ in the rate of increase in global heat content rather than ΔN, but these two variables have virtually identical values in the real world, and should do in AOGCMs”.
Elsewhere you will find that this is a positive number, if you care to look for it.

The global energy budget as the first differential energy storage equation. Equilibrium is when energy in equals energy out and there is no change in planetary energy content – Δ(heat & work) is zero.

Δ(heat & work) = energy in – energy out

Energy is stored 90% in the oceans. Equilibrium happens at the inflection points of ocean heat – both bi-annually and in the running mean in 2008. The imbalance is negative to 2008 – and positive since.

There is no other definition – and there is a difference between data and narrative. Only data counts.

Robert I Ellison: Equilibrium is when energy in equals energy out and there is no change in planetary energy content – Δ(heat & work) is zero.

That is not the definition of equilibrium. “Equilibrium” is when energy flow stops. The difference matters: the formal definition is the one used in the derivation of the Clausius-Clapeyron relation (this is explained in Pierrehumbert’s book “Principles of Planetary Climate.) C-C is applied during conditions of energy transfer, such as when clouds are forming above non-dry Earth surface, and some other occasions when it is known to be inaccurate.

Sorry to readers for the extra post. No more on this thread I promise.

Whatever – ECS is where the assumed radiative imbalance is balanced. You may define it in some pedantically misguided way as steady state rather than a physical, thermal equilibrium – but that isn’t the relevant issue. It just adds to the fog of misunderstanding.

“”matthewrmarler | April 19, 2017 at 12:28 pm |
Robert I Ellison: Equilibrium is when energy in equals energy out and there is no change in planetary energy content – Δ(heat & work) is zero.
That is not the definition of equilibrium. “Equilibrium” is when energy flow stops.”
Mathew we can all define equilibrium in different ways and if you wish to define it in a particular way yourself or choose a particular definition you would be right.
When energy flow stops is not a particularly good definition of equilibrium of systems as talked about here. You are defining one system only, one with no entropy, only being of use in an abstract sense.
Thermodynamic systems with or without ECS , have a definition of the incoming energy for the system balancing the outgoing energy exactly.
Now while just as abstract and unreal it has the advantage of being used to describe a theoretical state of a system that does have energy inputs and outputs, hence is of use.
I think Robert is fine to use his definition in a way that a lot of other people use and understand. Thanks.

Robert I. Ellison You may define it in some pedantically misguided way as steady state rather than a physical, thermal equilibrium – but that isn’t the relevant issue.

I can live with that as long as the writer is clear and consistent (or writers are.) It should be remembered that the derivations of the Clausius-Clapeyron relation and the moist adiabatic lapse rate are derived for the condition of thermodynamic equilibrium, not a steady-state.

Nic, did anything get further discussed on Richardson’s claim last year that observational ECS was biased low due to HadCRUT using sea surface temp SST while the models used sea surface air temp SAT? Did you approach Richardson with the nighttime sea air temperature HadNMAT2 record and the modeled diurnal temperature range DTR that Ken calculated?

Ron, thanks for reminding me about the point Ken made, about ocean daily minimum air temperatures increasing faster than mean ones, in models. I didn’t take it up with Richardson – I doubt there would be any point in doing so – but I will seek to point it out in future work.

Thanks Nic. For others, Richardson et al. (2016) claimed that the warming is worse than we think because the historic observational record of sea surface temperatures are ~2m below the surface rather the ~2m above the surface as on land. This discrepancy according to Richardson is partly why models run hotter. Models use surface air temp in both land and sea. Although that is undeniably true, we have a way to refute that it makes a difference. Although nighttime sea air temperature record, (there is no daytime one,) runs 4% higher than the 2m deep SST record used in all the global indexes, Ken Fritsch and I pointed out to Nic that the nighttime air temperatures represented Tmin, not Tavg. Then Ken showed the modeled difference between 100years trend of Tmin vs. Tavg happened to be 4%. Therefore there should be zero difference between seawater surface temp and the air immediately above it on average. Richardson was wrong there.

Uncertainty is still too large for the difference between 1.6 C and 2 C to be resolvable with much confidence. I think a median effective climate sensitivity estimate in that range is supported by the historical record to date, whether or not an infilled version of the temperature record or air temperatures over the ocean rather than SST are used. If the ratio of ECS to effective sensitivity (Armour’s ECS_infer) is the real world is above one, as it is in most CMIP5 models, then ECS might be above 2 C. But there is no real world evidence that the ratio is above one. And estimating ECS from the best studied and understood paleoclimate transition – from the LGM to the Holocene – using an energy budget approach gives a value in the 1.6 – 2.0 C range.

@TurbulentEddie “Climate are about how almost all places on earth are perpetually out of radiative balance and that imbalance is resolved by fluid flow from within:”

This is the wrong causality. The sphericity of earth leads to a differential heating of the tropic w.r.t the poles. This by itself is not what causes the imbalance at the TOA though. The extra heating at the tropics causes the atmosphere to be expanded there w.r.t the poles, thus inducing a poleward pressure gradient force that increases with height. This force induces poleward motion in the atmosphere which exchanges warm tropical fluid with cold polar fluid (simplification of course), thus decreasing the tropical temperature and increasing the polar temperatures. The lower (i.e. mixed) tropical temperature means that OLR is reduced w.r.t. to an equilibrium emission temperature with the insolation at those latitudes, and vice versa in the poles. Thus the imbalance at the TOA is due to the atmospheric (and oceanic) circulation, not the other way round.

Can you list the factors that control the climate vs the list of factors that control the weather? Are there items that are exclusive to one list and not the other? Is there overlap? Do you see where I am going with this?

Mesosphere funny claim in Wiki
“The main dynamic features in this region are strong zonal (East-West) winds, atmospheric tides, internal atmospheric gravity waves (commonly called “gravity waves”), and planetary waves. Most of these tides and waves start in the troposphere and lower stratosphere, and propagate to the mesosphere. In the mesosphere, gravity-wave amplitudes can become so large that the waves become unstable and dissipate. This dissipation deposits momentum into the mesosphere and largely drives global circulation.”
Nothing about ”
volcanic activity, global cloud coverage, global snow cover, atmospheric circulation patterns, sea surface temperatures and sea ice coverage.”

Here is a copy and paste from the wikipedia page for “Precession”; explaining the mechanism behind one of the 3 modes of variability associated with the earth-sun configuration i.e. the axial tilt. As you will see, this precession can be inferred from the position of the stars relative to the Earth and Sun, without the need for climate proxies.

“Axial precession is the movement of the rotational axis of an astronomical body, whereby the axis slowly traces out a cone. In the case of Earth, this type of precession is also known as the precession of the equinoxes, lunisolar precession, or precession of the equator. Earth goes through one such complete precessional cycle in a period of approximately 26,000 years or 1° every 72 years, during which the positions of stars will slowly change in both equatorial coordinates and ecliptic longitude. Over this cycle, Earth’s north axial pole moves from where it is now, within 1° of Polaris, in a circle around the ecliptic pole, with an angular radius of about 23.5°.

Hipparchus is claimed to be the earliest known astronomer to recognize and assess the precession of the equinoxes at about 1° per century (which is not far from the actual value for antiquity, 1.38°).[4] Caltech’s Swerdlow disputes Hipparchus’s knowledge of precession because Hipparchus apparently did not necessarily indicate anything like a motion of the entire sphere of the fixed stars with respect to the equinoxes.[5] The precession of Earth’s axis was later explained by Newtonian physics. Being an oblate spheroid, Earth has a non-spherical shape, bulging outward at the equator. The gravitational tidal forces of the Moon and Sun apply torque to the equator, attempting to pull the equatorial bulge into the plane of the ecliptic, but instead causing it to precess. The torque exerted by the planets, particularly Jupiter, also plays a role.[6]”

Being the armchair philosopher that I am, what I see are terms being used that aren’t scientific, like long and short term, day to day, global, unspecific effects, temporary, and the like being applied after the fact, with no real understanding of what’s going on.

Thanks, Nic, for doing another thought provoking analysis of a relevant climate science paper and an additional thanks for keeping your replies on an informational level and away from those who might want to turn the discussion into a battle of personalities.

In reference to your comment below on the assumptions in using OLS regressions, we had a discussion about this at the Blackboard awhile back and I compared the use of Ordinary Least Squares and Total Least Squares for the Gregory method regression and as I recall there was a difference – but I need to go back and check again. Have you compared OLS and TLS in this regression?

Also the regression with the apparent break around 21 years would appear to make the regression amenable to segmented breakpoint regression. Is there any conjecture or theory put forth to explain this break?

One further comment I have deals with work I have been doing with Empirical Mode Decomposition (EMD) and its improved versions of Ensemble Empirical Mode Decomposition (EEMD) and Complete Ensemble Empirical Mode Decomposition (CEEMD). The result of these analyses with instrumental global mean surface temperatures series using all the various temperature data sets leads to a reoccurring cyclical component of 60 to 70 years that greatly affects the derived secular trend that could be attributed to AGW. The method here makes no assumptions of a model and is empirical. It can handle non linear and non stationary series. When EMD and its variants are applied to the RCP 4.5 scenario over the historical period with CMIP5 climate models most model runs yield cyclical components of a relatively large range of frequencies that like the instrumental data affect the derived secular trend. That derived trends for observed and modeled series are almost always smaller than those conventionally derived and should significantly decrease the ECS and TCR estimates. There have been papers published on these EMD analyses with observed temperature series that essentially agree with what I have found, but I have not seen any interest in the climate science community as a whole of pursuing the possibility that there are natural cyclical components that could significantly affect the ECS and TCR estimations. Would you have any comments on this situation?

It also assumes, by the use of OLS regression, that internal variability in the regressor variable T is small enough to be ignored. It further assumes that T and N (a) have been correctly adjusted by deducting their equilibrium absolute levels in preindustrial conditions; (b) that any drift in those levels is constant over time and has been correctly adjusted for; and (c) that any imbalance in N in equilibrium, due e.g. to energy leakage in the model, is independent of the model’s climate state. Estimation of ECS by running the simulation until equilibrium is also dependent on assumptions (b) and (c).

April’s anomaly looks like it will be low… perhaps lower than December 2016’s. Another land-based teaser. Expect first 1/4 OHC to be higher. El Niño is still the forecast, and we’re about to pass through the May threshold and will soon know. Regardless, President Trump is doing the exact opposite of what is required to bring back the Divine Wind and global cooling. Send all manufacturing jobs to China; give them all the coal money can buy. Burn your way to global cooling.

My answer is if the degree of solar magnitude change is great enough and long enough in duration it will cause the albedo of earth to increase due to an increase in major volcanic activity , global cloud/snow coverage.

At the same time overall sea surface temperatures should decline.

SOLAR PARAMETERS NEEDED

SOLAR FLUX 90 OR LESS WE HAVE THIS NOW.

COSMIC RAY COUNTS IN ACCESS OF 6500 UNITS WE HAVE THIS.

EUV LIGHT 100 UNTIS OR LESS WE HAVE THIS. UV light decline we have this.

Two items not yet reached yet are solar wind speed less then 350 km/sec and AP INDEX 5 or lower.

Once reached I expect global temperatures to fall but it is still a little early because(but not much ) the solar parameters within my criteria currently have just reached it in the last 6 months or so while two solar parameters have yet to fall.

I will say if global temperatures do not fall as the solar parameters I have called for come about (say enforce for a year or so ) I will have to admit to being wrong. This will all happen this year and next year in other words by the end of year 2018 I will know if what I have been saying has any merit or not.

I say this with the expectation of very low solar parameters.

I might be out to lunch but that is what I have concluded based on the historical climatic record versus solar activity.

JCH | April 19, 2017
“President Trump is doing the exact opposite of what is required to bring back the Divine Wind and global cooling. Send all manufacturing jobs to China; give them all the coal money can buy.”
If we were to look at this like AGW JCH you would find that CO2 rise [Also known as China building more coal power stations and increasing manufacturing ] was happening long before Trump came on the scene.
You seem to be doing a usual cherrypick, taking a time with a new President you do not like coming in, to blame him for a warming cause that has nothing to do with him and would continue regardless of what he does.
Thanks to your precious Paris Climate Accord which gave the chinese free rein.
By the way a heads up. if April’s anomaly looks like it will be low, as will be the next 6 months courtesy of the recent La Nina and the flow on effect. one would expect sea ice extent levels, like DMI, to not fall precipitously.

JCH, “President Trump is doing the exact opposite of what is required to bring back the Divine Wind and global cooling.”

Jerry Brown of the land of fruits and nuts shares your concern. The EIA has emissions data by state and California has reduced their emissions by about 8% relative to 2005 levels. The national average reduction is a little over 9% so the state doing and spending the most to combat global warming is lagging in results.

I guess they deserve a participation award, but those crusty, old, angry, white, guys are more result oriented than the typical progressive.

By the way a heads up. if April’s anomaly looks like it will be low, as will be the next 6 months courtesy of the recent La Nina and the flow on effect. one would expect sea ice extent levels, like DMI, to not fall precipitously.

This is just abject physical nonsense. The PDO would have to flip negative for the next 6 months to be low. The PDO index went up slightly in March, so it remains positive going into the NH summer. IS it going to flip negative in the NH summer? Not likely.

The 2016 La Niña was hotter than hades because it was completely fenced in by warmth on all sides. You can forget about what La Niña events usually do.

” recent research has confirmed that CO2 forcing increases slightly faster than logarithmically with concentration,”

This “research” is calculation, not measurement, and it is clearly not physical. Measurements are unequivocal that forcing DECREASES approximately logarithmically with concentration. Unless you add lots of dubious feedbacks…

2. A steady-state will spontaneously relax towards equilibrium unless external work is done to main the state.

3. This work is termed dissipated energy (aka weather).

4. For a steady state in which 240W radiation enters at 5500K and exits at 200K, 96% on the incoming energy is dissipated, one high-energy photon having dissipated or been converted into 25 low-energy photons.

Ken,
Thanks for your comment. I’m glad you found this post interesting. You write:

“Have you compared OLS and TLS in this regression?

Also the regression with the apparent break around 21 years would appear to make the regression amenable to segmented breakpoint regression. Is there any conjecture or theory put forth to explain this break?”

Yes, I did try TLS regression on Gregory plot data a year or two ago. As one would expect, it gave a greater slope and lower ECS estimate than OLS regression. But TLS is only appropriate when the x and y variables have similar noise levels. Here, N has lower (fractional) internal variability than does T. A better choice when, as here, the noise levels in the two variables are (roughly) known is Deeming regression. I have tried that also. It makes quite a lot of difference (vs OLS) where the total chenge in T is fairly small.

The apparent break around year 20 can, perhaps surprisingly, be accounted for by a two time constant (TC) model like that described in Armour’s paper, with the first TC broadly in the region of 5 year and the second TC being 100+ years. The two TCs are usually associated with the heat capacity of the surface mixed-layer and deep ocean respectively.

The two time constants of the well mixed and deep ocean would appear as a reasonable explanation from this layperson’s viewpoint for the break at 20 years. I saw this break when I doing these Gregory regressions, but do recall at this time making any conjectures about the cause. I should go back and check whether there was a poorer fit for one or the other linear segments and whether all models had a breakpoint.

Nic, you did not comment on my EMD analysis. I have been looking for any evidence that would go against the empirical results here, i.e. that there are 60-70 year reoccurring cycles in the observed global mean surface temperature data. I’ll show some results here an EEMD analysis of the Old Karl (GHCN global mean with ocean ERSST v3b) and New Karl (GHCN global mean with Ocean ERSST v4).

In the table at the top of the linked image the EEMD and linear regressed breakpoint trends with confidence limits (determined by simulation using an AR model of the noise) are shown for five different time periods. The trends are all in degrees C per decade. It should first be noted that the trends either for EEMD or breakpoint are not significantly different between New and Old Karl for any of the five time periods. Secondly the difference in trends between the EEMD analysis and the breakpoint regression shows that for the critical 1975-2016 time period the EEMD trends are approximately 40% lower than the counterpart breakpoint linear regressed trends.

The graphs below the table depict the New and Old Karl trend and cyclical components and show both components as being much the same in shape and magnitude. The other two graphs show for the six components ln(component series variance) versus ln(component series period) with confidence intervals for the expected red and white noise of the series. The result is that the trend, noted as R, and the cyclical component, noted as 5, are determined to be statistically significant components while the other 4 components can be treated as noise.

Interesting but not shown is that for a difference series for New Karl minus Old Karl there are significant trend differences using linear breakpoint regression but with EEMD analysis all the components of the difference series are shown to be not significant.

Ken, Your EEMD analysis is certainly interesting; I commend you for undertaking it. Unfortunately, at present my understanding of EEMD methods is too limited to comment on your results, other than to say that I have little doubt there are real quasi-periodic multidecadal oscillations with a ~60-70 year timescale during the instrumental period. I believe the evidence points to these by entirely or largely natural, very likely linked to fluctuations in AMOC strength.
Re getting EEMD used in climate science, I’m unsure how easy this will be.

Re getting EEMD used in climate science, I’m unsure how easy this will be.

Nic, I’ll give the short version of a story that I have told at these blogs before and relates to how I was introduced to EEMD. I had several email exchanges with the authors of the Karl paper that incorporated the use of ERSST v4 in its GMST. I was promoting using Singular Spectrum Analysis (SSA) in looking at the newer and older versions GHCN and the Karl authors were suggesting the use of EMD. I later found through simulations that SSA could not resolve cyclical components in series like the GMST.

While exchanging emails I did a quick study of EMD and found that the Karl authors were not using the separations correctly and wanted to retain the combined trend and cyclical components as trend. When I showed them that their approach was wrong with techniques from papers written by the inventor of EMD (yes, it is patented https://www.google.com/patents/US6862558 ) Norden Huang, the Karl authors stopped the email exchanges.

“The real questions seem to be why do AOGCMs simulate very different warming patterns under increased CO2 concentration than those that have actually occurred during the historical period, and why do their net feedback strengths differ so much between these warming patterns.”

As a matter of scientific rigor, I would like to see more comparisons of GCMs to naive trends in these patterns. As forecasting scientists and coastal planning engineers have pointed out in the peer-reviewed literature, forecasts that cannot outperform naive trends are not a suitable basis for any long-term policy.

Maybe I am missing the point, but what makes nonlinear systems interesting is that they don’t behave like linear systems, which:

Either all converge to a point, or diverge to infinity.

This interesting behaviour of nonlinear systems is directly a result of the fact that a system which begins to run away due to a sensitivity very soon sees a decrease in that sensitivity and a countering sensitivity in the opposite direction.

Unless the terminology of this whole debate is throwing me, the whole thing seems like yet another eye rolling event.

Nic Lewis — Do you have a chart (or link to) that summarizes all the major estimates of TCR? For example, I saw a chart like this once, where my recollection (which could very well be wrong) was that Gavin Schmidt’s estimate to his low-end range agreed with your and Dr. Curry’s estimate. Thanks.

Stephen,
Sorry, I don’t at present have such a chart. But energy budget studies provide the most robust TCR estimates, and the the two most often cited such studies – Otto et al 2013 and Lewis & Curry 2015, came up with identical TCR estimates, both of 1.33 C. An update of the Lewis & Curry estimate, using data to 2015 rather than 2011, and a later version of the HadCRUT4 global tempersture record, was almost identical.

These simulations start from an equilibrium preindustrial state and usually cover 150 years.

Fine, fine but… what if I told you that an equilibrium temperature response caused by the impact of humanity will take thousands of years and will be minor compared to responses over the next hundreds of years that humans will in hindsight consider to have been good?

“The real questions seem to be why do AOGCMs simulate very different warming patterns under increased CO2 concentration than those that have actually occurred during the historical period, and why do their net feedback strengths differ so much between these warming patterns.”

A reference for steady-state: Kondepudi and Prigogine: Modern Thermodynamics. It lacks an index entry for “steady state”, but uses “steady state” with reference to “stationary” states, which are indexed.

In chemical kinetics, “steady state” is the assumption behind the derivation of the widely used Michaelis-Menten approximation to rate equations (that is, the Michaelis-Menten equation is exact for the steady state case, but may be a useful approximation to the non-steady-state case. n Bailey and Ollis, Biochemical Engineering Fundamentals, this is in section 3.2.1; they use the phrase “quasi steady-state approximation”, and show with a computed example that it gives results in agreement with corresponding exact diff eqns.

I should note, in fairness to those I have criticized, that Bailey and Ollis also use “equilibrium” in a case where there is balanced interchange between two compartments (p 100, eqn 3.4a, and discussion at bottom of page.) So perhaps the usage of “equilibrium” that I deprecated is more widespread than I thought. Maybe universal?

There is a pretty long list of types of equilibrium and “steady states.” As Robert mentioned radiant equilibrium at the top of the atmosphere is the main one in greenhouse gas/ global warming theory and that is an averaged equilibrium over some time frame since we are dealing with a complex planetary scale system. So it is really more interesting how much error there can be if you don’t use the most appropriate time frame.

Rosenthal et al. indicated there are multi-century scale imbalances which can be significant with an already small imbalance of 0.6 Wm-2 +/- o,4 or so. I doubt that would have much impact on TCR, but it could reduce ECS.

The dry atmospheric lapse rate is derived assuming an adiabatic process – defined as no transfer of heat from a parcel of rising air to the surrounding air. The Clausius-Clapeyron relationship is derived assuming an isolated system. Not quite the same thing.

Neither are directly relevant to ECS or energy imbalances at TOA – where radiative equilibrium is defined in the strict mathematical – rather than thermodynamic – sense of energy in and energy out being equal. The system tends to return to energy equilibrium given the usual energy dynamics. Adding CO2 to the atmosphere results in more energy retained in the atmosphere and a temporary reduction in energy out. The immediate atmospheric temperature increase is the transient climate response. The equilibrium sensitivity occurs when oceans warm sufficiently to increase surface emissions of IR radiation and radiative equilibrium at TOA is restored.

From the first law of thermodynamics – energy is conserved –

Δ(heat & work) = energy in – energy out

On a planetary level energy can only be gained or lost as electromagnetic radiation at toa. There are some minor terms that are neglected – but the first differential global energy storage equation is reasonably precise.

TCR and ECS make sense only in a smoothly evolving climate. This is not the case on decadal to millenial scales. The theory of abrupt climate change suggests that the system is pushed by greenhouse gas changes and warming – as well as solar intensity and Earth orbital eccentricities – past a threshold at which stage the components start to interact chaotically in multiple and changing negative and positive feedbacks – as tremendous energies cascade through powerful subsystems. Some of these changes have a regularity within broad limits and the planet responds with a broad regularity in changes of ice, cloud, Atlantic thermohaline circulation and ocean and atmospheric circulation.

Dynamic climate sensitivity implies the potential for a small push to initiate a large shift. Climate in this theory of abrupt change is an emergent property of the shift in global energies as the system settles down into a new climate state. The traditional definition of climate sensitivity as a temperature response to changes in CO2 makes sense only in periods between climate shifts – as climate changes at shifts are internally generated. Climate evolution is discontinuous at the scale of decades and longer.

The problem in a chaotic climate then becomes not one of quantifying climate sensitivity in a smoothly evolving climate but of predicting the onset of abrupt climate shifts and their implications for climate and society. The problem of abrupt climate change on multi-decadal scales is of the most immediate significance.

There are three questions that remain. How do these energy terms change, how sensitive is the planetary temperature to forcing and how long does it take the oceans to equilibriate in the mathematical sense?

The answer to the first is that energy out varies substantially with changes in ocean and atmospheric circulation and resultant changes in both planetary albedo and IR emissions.

Oceans warm and cool on an annual basis quite substantially due to north/south asymmetry. Even the neglected term of matter conversion to energy in the Earth’s interior is many orders of magnitude greater than the instantaneous increase in greenhouse gas forcing (0.45W/m2 >> 1E-9W/m2). That the atmosphere warms and retains additional heat in the oceans seems more likely than a slow warming of the oceans due to a warmer atmosphere. Thus TCR and ECS are equal and no imbalance accumulates at toa. The world is simply warmer and the pipeline is empty.

In the very long term – there is a 25W/m2 change in forcing between the last glacial max and the current interstadial – for a 5 degree C temperature increase. It suggests a climate response of 0.2 degrees C per 1W/m2 change in forcing. For a doubling of CO2 in the atmosphere this is 0.74 degrees C warming. Not very sensitive then – but It makes sense only in the context of a control variable in a chaotic system. This latter is what we need to better understand.

All this is – as I keep saying – not relevant at all to policy. The world is moving to sequester 360 billion tonnes of CO2 for many other reasons – and there will be a transition to cheap and abundant 21st century energy sources within decades.